OVs can also be classified from many different perspectives. A vortex beam (VB) may possess an integer or fractional TC [1]}. Therefore, VBs are divided into two categories:integer and fractional VBs.
An integer VB has an annular intensity distribution with a dark central node produced by the phase singularity, while a fractional VB is devoid of rotational symmetry due to a distortion at the discontinuous
phase. It is able to decompose a fractional VB into an orthogonal set of integer modes [2]}. Further considering the radial intensity distribution, a series of different VBs
were obtained theoretically and experimentally, including Laguerre-Gaussian beams [3]}, Bessel-Gaussian beams [4]}, Mathieu beams[5]}, perfect vortex beams [6]}, anomalous vortex beams [7]}, etc. Meanwhile, in addition to the above mentioned beams with a single vortex, VBs which contain multiple
singularities may also provide novel types of OAM. VBs embedded with specific vortex arrays were generated and modulated, such as Hermite-Laguerre-Gaussian beams [8]}, helical-Ince beams[9]}, SU(2) geometric modes[10]}, and high-power
laser modes in a nearly hemispherical cavity[11]}. With such a wide range of choices on VBs, researchers can implement related applications under distinct circumstances.
